Fault Detection for Shipboard Monitoring – Volterra Kernel and Hammerstein Model Approaches Zoran Lajic * , Mogens Blanke **,*** and Ulrik Dam Nielsen * * Technical University of Denmark, Department of Mechanical Engineering, Section of Coastal, Maritime and Structural Eng. Build. 403, 2800-Kgs. Lyngby, Denmark {zl@mek.dtu.dk}, {udn@mek.dtu.dk} ** Technical University of Denmark, Department of Electrical Engineering, Automation and Control Group Build. 326, 2800-Kgs. Lyngby, Denmark {mb@elektro.dtu.dk} *** Norwegian University of Technology and Science, Centre for Ships and Ocean Structures 7491 Trondheim, Norway Abstract: In this paper nonlinear fault detection for in-service monitoring and decision support systems for ships will be presented. The ship is described as a nonlinear system, and the stochastic wave elevation and the associated ship responses are conveniently modelled in frequency domain. The transformation from time domain to frequency domain has been conducted by use of Volterra theory. The paper takes as an example fault detection of a containership on which a decision support system has been installed. Copyright © 2009 IFAC. 1. INTRODUCTION The SeaSense system (Nielsen et al., 2006) has been installed on several containerships and navy vessels. The system provides an estimation of the actual sea state, information about the longitudinal hull-girder loading, sea-keeping performance of the ship, and decision support on how to operate the ship within acceptable limits. The system is able to identify critical forthcoming events and to give advice regarding speed and course changes to decrease the wave- induced loads. The SeaSense system sensors, sketched in Fig. 1, includes sensors, which are used to estimate hull stresses and predict wave loads, with the purpose of avoiding critical levels of hull stresses and ship motions. Detection of sensor faults is critical for the correct operation of the system. Several papers deal with maritime applications of fault- tolerant control systems. For example, a fault-tolerant sensor- fusion and control system for ship station keeping has been shown in (Blanke et al., 2005). The present paper investigates possibilities to employ fault- diagnosis techniques to improve the dependability of the SeaSense system. Sensor fault diagnosis is considered using available measurements: vertical acceleration, heave, pitch, roll, wave elevation and relative wave height (distance between the deck and the water surface). The wave elevation could be obtained using the SeaSense system and it has been. – artificially – included in the sensor fault detection pro- cedure as a virtual sensor. The ship is a nonlinear system by nature. A linear model cannot be adopted for the ship sailing in heavy weather due to large roll angles and nonlinear vertical motions. Instead, a Volterra series approach is used to arrive at residuals for fault diagnosis. The Volterra theory is based on an approximation and the model is used to investigate and justify a possible implementation of this theory. The results are compared with the residuals obtained by a Hammerstein model, which can be realized without any approximation. It is worth noting that is not always possible to use Hammerstein model(s). Hammerstein model(s) can be implemented only for systems, which have a particular separation between a static nonlinearity and a part with linear dynamics. Fig.1: Onboard sensor arrangement 2. STRUCTURAL ANALYSIS For the sensor fault detection, there is a need to find physical relations between measured values. The SeaSense system has at its disposal several measurements: vertical acceleration, heave, pitch, roll, wave elevation and relative wave height. In case sea state estimation is conducted by a ship-wave buoy analogy (e.g. Nielsen, 2006 and 2008), it is sufficient to use